A temporal Galerkin discretization of the charge-current continuity equation

In time domain boundary integral equations, scattered fields are computed from a priori unknown electric current and charge densities. In many implementations, the charge density is eliminated from the integral equation prior to discretization, using the charge-current continuity equation. In this contribution, the charge density is explicitly discretized, and the continuity equation is weakly enforced by a space-time Galerkin procedure, leading to a simpler and more consistent implementation. The effects of this discretization scheme on the stability and the accuracy of the resulting solution method are discussed.